Linear regression is widely used
to estimate financial asset pricing models, where the dependent variable is
the (excess) return on a stock.
Yet stock returns are distributed far from Gaussian, so that a Gaussian regression model is
mis-specified.
To illustrate the regression copula model it is used to model
monthly excess returns on American Express Company (which has NYSE ticker symbol “AXP”) using data from 07/1972 to 10/2020.
The marginal distribution is assumed invariant with respect to observation,
so that \(F_{Y_i}(y_i)=G(y_i)\) . A three parameter asymmetric Laplace distribution is
fit,
which better accounts for the distribution of returns as highlighted
by [1]} and [2]}. Figure REF  plots the
density of the fitted margin, which is both asymmetric and has very heavy tails.
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